The experiment with phase inversion and phase-inverted echo-amplitude detected nutation (PEANUT) was introduced in the nuclear quadrupole resonance (NQR). Formulas were obtained describing the NQR (I=3/2) experiment. Exemplary experiments are provided confirming the predicted particularities of the PEANUT spectra in NQR Cl-35. It is proposed to apply the method for the purpose of determination the asymmetry parameter of the electric field gradient (EFG) tensor in powders with the help of the analysis of PEANUT interferograms. Application of two-dimensional PEANUT experiments, in which the nutation frequencies correlate with the resonance NQR frequencies, can substantially simplify the interpretation of complex spectra.